// Copyright 2014 the V8 project authors. All rights reserved.
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file.

#include <iomanip>

#include "src/compiler/types.h"

#include "src/handles-inl.h"
#include "src/objects-inl.h"
#include "src/ostreams.h"

namespace v8 {
namespace internal {
    namespace compiler {

        // -----------------------------------------------------------------------------
        // Range-related helper functions.

        bool RangeType::Limits::IsEmpty() { return this->min > this->max; }

        RangeType::Limits RangeType::Limits::Intersect(Limits lhs, Limits rhs)
        {
            DisallowHeapAllocation no_allocation;
            Limits result(lhs);
            if (lhs.min < rhs.min)
                result.min = rhs.min;
            if (lhs.max > rhs.max)
                result.max = rhs.max;
            return result;
        }

        RangeType::Limits RangeType::Limits::Union(Limits lhs, Limits rhs)
        {
            DisallowHeapAllocation no_allocation;
            if (lhs.IsEmpty())
                return rhs;
            if (rhs.IsEmpty())
                return lhs;
            Limits result(lhs);
            if (lhs.min > rhs.min)
                result.min = rhs.min;
            if (lhs.max < rhs.max)
                result.max = rhs.max;
            return result;
        }

        bool Type::Overlap(const RangeType* lhs, const RangeType* rhs)
        {
            DisallowHeapAllocation no_allocation;
            return !RangeType::Limits::Intersect(RangeType::Limits(lhs),
                RangeType::Limits(rhs))
                        .IsEmpty();
        }

        bool Type::Contains(const RangeType* lhs, const RangeType* rhs)
        {
            DisallowHeapAllocation no_allocation;
            return lhs->Min() <= rhs->Min() && rhs->Max() <= lhs->Max();
        }

        // -----------------------------------------------------------------------------
        // Min and Max computation.

        double Type::Min() const
        {
            DCHECK(this->Is(Number()));
            DCHECK(!this->Is(NaN()));
            if (this->IsBitset())
                return BitsetType::Min(this->AsBitset());
            if (this->IsUnion()) {
                double min = +V8_INFINITY;
                for (int i = 1, n = AsUnion()->Length(); i < n; ++i) {
                    min = std::min(min, AsUnion()->Get(i).Min());
                }
                Type bitset = AsUnion()->Get(0);
                if (!bitset.Is(NaN()))
                    min = std::min(min, bitset.Min());
                return min;
            }
            if (this->IsRange())
                return this->AsRange()->Min();
            DCHECK(this->IsOtherNumberConstant());
            return this->AsOtherNumberConstant()->Value();
        }

        double Type::Max() const
        {
            DCHECK(this->Is(Number()));
            DCHECK(!this->Is(NaN()));
            if (this->IsBitset())
                return BitsetType::Max(this->AsBitset());
            if (this->IsUnion()) {
                double max = -V8_INFINITY;
                for (int i = 1, n = this->AsUnion()->Length(); i < n; ++i) {
                    max = std::max(max, this->AsUnion()->Get(i).Max());
                }
                Type bitset = this->AsUnion()->Get(0);
                if (!bitset.Is(NaN()))
                    max = std::max(max, bitset.Max());
                return max;
            }
            if (this->IsRange())
                return this->AsRange()->Max();
            DCHECK(this->IsOtherNumberConstant());
            return this->AsOtherNumberConstant()->Value();
        }

        // -----------------------------------------------------------------------------
        // Glb and lub computation.

        // The largest bitset subsumed by this type.
        Type::bitset Type::BitsetGlb() const
        {
            DisallowHeapAllocation no_allocation;
            // Fast case.
            if (IsBitset()) {
                return AsBitset();
            } else if (IsUnion()) {
                SLOW_DCHECK(AsUnion()->Wellformed());
                return AsUnion()->Get(0).BitsetGlb() | AsUnion()->Get(1).BitsetGlb(); // Shortcut.
            } else if (IsRange()) {
                bitset glb = BitsetType::Glb(AsRange()->Min(), AsRange()->Max());
                return glb;
            } else {
                return BitsetType::kNone;
            }
        }

        // The smallest bitset subsuming this type, possibly not a proper one.
        Type::bitset Type::BitsetLub() const
        {
            DisallowHeapAllocation no_allocation;
            if (IsBitset())
                return AsBitset();
            if (IsUnion()) {
                // Take the representation from the first element, which is always
                // a bitset.
                int bitset = AsUnion()->Get(0).BitsetLub();
                for (int i = 0, n = AsUnion()->Length(); i < n; ++i) {
                    // Other elements only contribute their semantic part.
                    bitset |= AsUnion()->Get(i).BitsetLub();
                }
                return bitset;
            }
            if (IsHeapConstant())
                return AsHeapConstant()->Lub();
            if (IsOtherNumberConstant()) {
                return AsOtherNumberConstant()->Lub();
            }
            if (IsRange())
                return AsRange()->Lub();
            if (IsTuple())
                return BitsetType::kOtherInternal;
            UNREACHABLE();
        }

        // TODO(neis): Once the broker mode kDisabled is gone, change the input type to
        // MapRef and get rid of the HeapObjectType class.
        template <typename MapRefLike>
        Type::bitset BitsetType::Lub(const MapRefLike& map)
        {
            switch (map.instance_type()) {
            case CONS_STRING_TYPE:
            case CONS_ONE_BYTE_STRING_TYPE:
            case THIN_STRING_TYPE:
            case THIN_ONE_BYTE_STRING_TYPE:
            case SLICED_STRING_TYPE:
            case SLICED_ONE_BYTE_STRING_TYPE:
            case EXTERNAL_STRING_TYPE:
            case EXTERNAL_ONE_BYTE_STRING_TYPE:
            case UNCACHED_EXTERNAL_STRING_TYPE:
            case UNCACHED_EXTERNAL_ONE_BYTE_STRING_TYPE:
            case STRING_TYPE:
            case ONE_BYTE_STRING_TYPE:
                return kString;
            case EXTERNAL_INTERNALIZED_STRING_TYPE:
            case EXTERNAL_ONE_BYTE_INTERNALIZED_STRING_TYPE:
            case UNCACHED_EXTERNAL_INTERNALIZED_STRING_TYPE:
            case UNCACHED_EXTERNAL_ONE_BYTE_INTERNALIZED_STRING_TYPE:
            case INTERNALIZED_STRING_TYPE:
            case ONE_BYTE_INTERNALIZED_STRING_TYPE:
                return kInternalizedString;
            case SYMBOL_TYPE:
                return kSymbol;
            case BIGINT_TYPE:
                return kBigInt;
            case ODDBALL_TYPE:
                switch (map.oddball_type()) {
                case OddballType::kNone:
                    break;
                case OddballType::kHole:
                    return kHole;
                case OddballType::kBoolean:
                    return kBoolean;
                case OddballType::kNull:
                    return kNull;
                case OddballType::kUndefined:
                    return kUndefined;
                case OddballType::kUninitialized:
                case OddballType::kOther:
                    // TODO(neis): We should add a kOtherOddball type.
                    return kOtherInternal;
                }
                UNREACHABLE();
            case HEAP_NUMBER_TYPE:
                return kNumber;
            case JS_OBJECT_TYPE:
            case JS_ARGUMENTS_TYPE:
            case JS_ERROR_TYPE:
            case JS_GLOBAL_OBJECT_TYPE:
            case JS_GLOBAL_PROXY_TYPE:
            case JS_API_OBJECT_TYPE:
            case JS_SPECIAL_API_OBJECT_TYPE:
                if (map.is_undetectable()) {
                    // Currently we assume that every undetectable receiver is also
                    // callable, which is what we need to support document.all.  We
                    // could add another Type bit to support other use cases in the
                    // future if necessary.
                    DCHECK(map.is_callable());
                    return kOtherUndetectable;
                }
                if (map.is_callable()) {
                    return kOtherCallable;
                }
                return kOtherObject;
            case JS_ARRAY_TYPE:
                return kArray;
            case JS_VALUE_TYPE:
            case JS_MESSAGE_OBJECT_TYPE:
            case JS_DATE_TYPE:
#ifdef V8_INTL_SUPPORT
            case JS_INTL_V8_BREAK_ITERATOR_TYPE:
            case JS_INTL_COLLATOR_TYPE:
            case JS_INTL_DATE_TIME_FORMAT_TYPE:
            case JS_INTL_LIST_FORMAT_TYPE:
            case JS_INTL_LOCALE_TYPE:
            case JS_INTL_NUMBER_FORMAT_TYPE:
            case JS_INTL_PLURAL_RULES_TYPE:
            case JS_INTL_RELATIVE_TIME_FORMAT_TYPE:
            case JS_INTL_SEGMENT_ITERATOR_TYPE:
            case JS_INTL_SEGMENTER_TYPE:
#endif // V8_INTL_SUPPORT
            case JS_CONTEXT_EXTENSION_OBJECT_TYPE:
            case JS_GENERATOR_OBJECT_TYPE:
            case JS_ASYNC_FUNCTION_OBJECT_TYPE:
            case JS_ASYNC_GENERATOR_OBJECT_TYPE:
            case JS_MODULE_NAMESPACE_TYPE:
            case JS_ARRAY_BUFFER_TYPE:
            case JS_ARRAY_ITERATOR_TYPE:
            case JS_REGEXP_TYPE: // TODO(rossberg): there should be a RegExp type.
            case JS_REGEXP_STRING_ITERATOR_TYPE:
            case JS_TYPED_ARRAY_TYPE:
            case JS_DATA_VIEW_TYPE:
            case JS_SET_TYPE:
            case JS_MAP_TYPE:
            case JS_SET_KEY_VALUE_ITERATOR_TYPE:
            case JS_SET_VALUE_ITERATOR_TYPE:
            case JS_MAP_KEY_ITERATOR_TYPE:
            case JS_MAP_KEY_VALUE_ITERATOR_TYPE:
            case JS_MAP_VALUE_ITERATOR_TYPE:
            case JS_STRING_ITERATOR_TYPE:
            case JS_ASYNC_FROM_SYNC_ITERATOR_TYPE:
            case JS_FINALIZATION_GROUP_TYPE:
            case JS_FINALIZATION_GROUP_CLEANUP_ITERATOR_TYPE:
            case JS_WEAK_MAP_TYPE:
            case JS_WEAK_REF_TYPE:
            case JS_WEAK_SET_TYPE:
            case JS_PROMISE_TYPE:
            case WASM_EXCEPTION_TYPE:
            case WASM_GLOBAL_TYPE:
            case WASM_INSTANCE_TYPE:
            case WASM_MEMORY_TYPE:
            case WASM_MODULE_TYPE:
            case WASM_TABLE_TYPE:
            case WEAK_CELL_TYPE:
                DCHECK(!map.is_callable());
                DCHECK(!map.is_undetectable());
                return kOtherObject;
            case JS_BOUND_FUNCTION_TYPE:
                DCHECK(!map.is_undetectable());
                return kBoundFunction;
            case JS_FUNCTION_TYPE:
                DCHECK(!map.is_undetectable());
                return kFunction;
            case JS_PROXY_TYPE:
                DCHECK(!map.is_undetectable());
                if (map.is_callable())
                    return kCallableProxy;
                return kOtherProxy;
            case MAP_TYPE:
            case ALLOCATION_SITE_TYPE:
            case ACCESSOR_INFO_TYPE:
            case SHARED_FUNCTION_INFO_TYPE:
            case FUNCTION_TEMPLATE_INFO_TYPE:
            case FUNCTION_TEMPLATE_RARE_DATA_TYPE:
            case ACCESSOR_PAIR_TYPE:
            case EMBEDDER_DATA_ARRAY_TYPE:
            case FIXED_ARRAY_TYPE:
            case HASH_TABLE_TYPE:
            case ORDERED_HASH_MAP_TYPE:
            case ORDERED_HASH_SET_TYPE:
            case ORDERED_NAME_DICTIONARY_TYPE:
            case NAME_DICTIONARY_TYPE:
            case GLOBAL_DICTIONARY_TYPE:
            case NUMBER_DICTIONARY_TYPE:
            case SIMPLE_NUMBER_DICTIONARY_TYPE:
            case STRING_TABLE_TYPE:
            case EPHEMERON_HASH_TABLE_TYPE:
            case WEAK_FIXED_ARRAY_TYPE:
            case WEAK_ARRAY_LIST_TYPE:
            case FIXED_DOUBLE_ARRAY_TYPE:
            case FEEDBACK_METADATA_TYPE:
            case BYTE_ARRAY_TYPE:
            case BYTECODE_ARRAY_TYPE:
            case OBJECT_BOILERPLATE_DESCRIPTION_TYPE:
            case ARRAY_BOILERPLATE_DESCRIPTION_TYPE:
            case DESCRIPTOR_ARRAY_TYPE:
            case TRANSITION_ARRAY_TYPE:
            case FEEDBACK_CELL_TYPE:
            case CLOSURE_FEEDBACK_CELL_ARRAY_TYPE:
            case FEEDBACK_VECTOR_TYPE:
            case PROPERTY_ARRAY_TYPE:
            case FOREIGN_TYPE:
            case SCOPE_INFO_TYPE:
            case SCRIPT_CONTEXT_TABLE_TYPE:
            case AWAIT_CONTEXT_TYPE:
            case BLOCK_CONTEXT_TYPE:
            case CATCH_CONTEXT_TYPE:
            case DEBUG_EVALUATE_CONTEXT_TYPE:
            case EVAL_CONTEXT_TYPE:
            case FUNCTION_CONTEXT_TYPE:
            case MODULE_CONTEXT_TYPE:
            case NATIVE_CONTEXT_TYPE:
            case SCRIPT_CONTEXT_TYPE:
            case WITH_CONTEXT_TYPE:
            case SCRIPT_TYPE:
            case CODE_TYPE:
            case PROPERTY_CELL_TYPE:
            case MODULE_TYPE:
            case MODULE_INFO_ENTRY_TYPE:
            case CELL_TYPE:
            case PREPARSE_DATA_TYPE:
            case UNCOMPILED_DATA_WITHOUT_PREPARSE_DATA_TYPE:
            case UNCOMPILED_DATA_WITH_PREPARSE_DATA_TYPE:
                return kOtherInternal;

            // Remaining instance types are unsupported for now. If any of them do
            // require bit set types, they should get kOtherInternal.
            case MUTABLE_HEAP_NUMBER_TYPE:
            case FREE_SPACE_TYPE:
#define FIXED_TYPED_ARRAY_CASE(Type, type, TYPE, ctype) \
    case FIXED_##TYPE##_ARRAY_TYPE:

                TYPED_ARRAYS(FIXED_TYPED_ARRAY_CASE)
#undef FIXED_TYPED_ARRAY_CASE
            case FILLER_TYPE:
            case ACCESS_CHECK_INFO_TYPE:
            case ASM_WASM_DATA_TYPE:
            case CALL_HANDLER_INFO_TYPE:
            case INTERCEPTOR_INFO_TYPE:
            case OBJECT_TEMPLATE_INFO_TYPE:
            case ALLOCATION_MEMENTO_TYPE:
            case ALIASED_ARGUMENTS_ENTRY_TYPE:
            case PROMISE_CAPABILITY_TYPE:
            case PROMISE_REACTION_TYPE:
            case CLASS_POSITIONS_TYPE:
            case DEBUG_INFO_TYPE:
            case STACK_FRAME_INFO_TYPE:
            case STACK_TRACE_FRAME_TYPE:
            case SMALL_ORDERED_HASH_MAP_TYPE:
            case SMALL_ORDERED_HASH_SET_TYPE:
            case SMALL_ORDERED_NAME_DICTIONARY_TYPE:
            case PROTOTYPE_INFO_TYPE:
            case INTERPRETER_DATA_TYPE:
            case TUPLE2_TYPE:
            case TUPLE3_TYPE:
            case ENUM_CACHE_TYPE:
            case WASM_DEBUG_INFO_TYPE:
            case WASM_EXCEPTION_TAG_TYPE:
            case WASM_EXPORTED_FUNCTION_DATA_TYPE:
            case LOAD_HANDLER_TYPE:
            case STORE_HANDLER_TYPE:
            case ASYNC_GENERATOR_REQUEST_TYPE:
            case CODE_DATA_CONTAINER_TYPE:
            case CALLBACK_TASK_TYPE:
            case CALLABLE_TASK_TYPE:
            case PROMISE_FULFILL_REACTION_JOB_TASK_TYPE:
            case PROMISE_REJECT_REACTION_JOB_TASK_TYPE:
            case PROMISE_RESOLVE_THENABLE_JOB_TASK_TYPE:
            case FINALIZATION_GROUP_CLEANUP_JOB_TASK_TYPE:
                UNREACHABLE();
            }
            UNREACHABLE();
        }

        // Explicit instantiation.
        template Type::bitset BitsetType::Lub<MapRef>(const MapRef& map);

        Type::bitset BitsetType::Lub(double value)
        {
            DisallowHeapAllocation no_allocation;
            if (IsMinusZero(value))
                return kMinusZero;
            if (/*std::*/isnan(value))
                return kNaN;
            if (IsUint32Double(value) || IsInt32Double(value))
                return Lub(value, value);
            return kOtherNumber;
        }

        // Minimum values of plain numeric bitsets.
        const BitsetType::Boundary BitsetType::BoundariesArray[] = {
            { kOtherNumber, kPlainNumber, -V8_INFINITY },
            { kOtherSigned32, kNegative32, kMinInt },
            { kNegative31, kNegative31, -0x40000000 },
            { kUnsigned30, kUnsigned30, 0 },
            { kOtherUnsigned31, kUnsigned31, 0x40000000 },
            { kOtherUnsigned32, kUnsigned32, 0x80000000 },
            { kOtherNumber, kPlainNumber, static_cast<double>(kMaxUInt32) + 1 }
        };

        const BitsetType::Boundary* BitsetType::Boundaries() { return BoundariesArray; }

        size_t BitsetType::BoundariesSize()
        {
            // Windows doesn't like arraysize here.
            // return arraysize(BoundariesArray);
            return 7;
        }

        Type::bitset BitsetType::ExpandInternals(Type::bitset bits)
        {
            DCHECK_IMPLIES(bits & kOtherString, (bits & kString) == kString);
            DisallowHeapAllocation no_allocation;
            if (!(bits & kPlainNumber))
                return bits; // Shortcut.
            const Boundary* boundaries = Boundaries();
            for (size_t i = 0; i < BoundariesSize(); ++i) {
                DCHECK(BitsetType::Is(boundaries[i].internal, boundaries[i].external));
                if (bits & boundaries[i].internal)
                    bits |= boundaries[i].external;
            }
            return bits;
        }

        Type::bitset BitsetType::Lub(double min, double max)
        {
            DisallowHeapAllocation no_allocation;
            int lub = kNone;
            const Boundary* mins = Boundaries();

            for (size_t i = 1; i < BoundariesSize(); ++i) {
                if (min < mins[i].min) {
                    lub |= mins[i - 1].internal;
                    if (max < mins[i].min)
                        return lub;
                }
            }
            return lub | mins[BoundariesSize() - 1].internal;
        }

        Type::bitset BitsetType::NumberBits(bitset bits) { return bits & kPlainNumber; }

        Type::bitset BitsetType::Glb(double min, double max)
        {
            DisallowHeapAllocation no_allocation;
            int glb = kNone;
            const Boundary* mins = Boundaries();

            // If the range does not touch 0, the bound is empty.
            if (max < -1 || min > 0)
                return glb;

            for (size_t i = 1; i + 1 < BoundariesSize(); ++i) {
                if (min <= mins[i].min) {
                    if (max + 1 < mins[i + 1].min)
                        break;
                    glb |= mins[i].external;
                }
            }
            // OtherNumber also contains float numbers, so it can never be
            // in the greatest lower bound.
            return glb & ~(kOtherNumber);
        }

        double BitsetType::Min(bitset bits)
        {
            DisallowHeapAllocation no_allocation;
            DCHECK(Is(bits, kNumber));
            DCHECK(!Is(bits, kNaN));
            const Boundary* mins = Boundaries();
            bool mz = bits & kMinusZero;
            for (size_t i = 0; i < BoundariesSize(); ++i) {
                if (Is(mins[i].internal, bits)) {
                    return mz ? std::min(0.0, mins[i].min) : mins[i].min;
                }
            }
            DCHECK(mz);
            return 0;
        }

        double BitsetType::Max(bitset bits)
        {
            DisallowHeapAllocation no_allocation;
            DCHECK(Is(bits, kNumber));
            DCHECK(!Is(bits, kNaN));
            const Boundary* mins = Boundaries();
            bool mz = bits & kMinusZero;
            if (BitsetType::Is(mins[BoundariesSize() - 1].internal, bits)) {
                return +V8_INFINITY;
            }
            for (size_t i = BoundariesSize() - 1; i-- > 0;) {
                if (Is(mins[i].internal, bits)) {
                    return mz ? std::max(0.0, mins[i + 1].min - 1) : mins[i + 1].min - 1;
                }
            }
            DCHECK(mz);
            return 0;
        }

        // static
        bool OtherNumberConstantType::IsOtherNumberConstant(double value)
        {
            // Not an integer, not NaN, and not -0.
            return !/*std::*/isnan(value) && !RangeType::IsInteger(value) && !IsMinusZero(value);
        }

        HeapConstantType::HeapConstantType(BitsetType::bitset bitset,
            const HeapObjectRef& heap_ref)
            : TypeBase(kHeapConstant)
            , bitset_(bitset)
            , heap_ref_(heap_ref)
        {
        }

        Handle<HeapObject> HeapConstantType::Value() const
        {
            return heap_ref_.object();
        }

        // -----------------------------------------------------------------------------
        // Predicates.

        bool Type::SimplyEquals(Type that) const
        {
            DisallowHeapAllocation no_allocation;
            if (this->IsHeapConstant()) {
                return that.IsHeapConstant() && this->AsHeapConstant()->Value().address() == that.AsHeapConstant()->Value().address();
            }
            if (this->IsOtherNumberConstant()) {
                return that.IsOtherNumberConstant() && this->AsOtherNumberConstant()->Value() == that.AsOtherNumberConstant()->Value();
            }
            if (this->IsRange()) {
                if (that.IsHeapConstant() || that.IsOtherNumberConstant())
                    return false;
            }
            if (this->IsTuple()) {
                if (!that.IsTuple())
                    return false;
                const TupleType* this_tuple = this->AsTuple();
                const TupleType* that_tuple = that.AsTuple();
                if (this_tuple->Arity() != that_tuple->Arity()) {
                    return false;
                }
                for (int i = 0, n = this_tuple->Arity(); i < n; ++i) {
                    if (!this_tuple->Element(i).Equals(that_tuple->Element(i)))
                        return false;
                }
                return true;
            }
            UNREACHABLE();
        }

        // Check if [this] <= [that].
        bool Type::SlowIs(Type that) const
        {
            DisallowHeapAllocation no_allocation;

            // Fast bitset cases
            if (that.IsBitset()) {
                return BitsetType::Is(this->BitsetLub(), that.AsBitset());
            }

            if (this->IsBitset()) {
                return BitsetType::Is(this->AsBitset(), that.BitsetGlb());
            }

            // (T1 \/ ... \/ Tn) <= T  if  (T1 <= T) /\ ... /\ (Tn <= T)
            if (this->IsUnion()) {
                for (int i = 0, n = this->AsUnion()->Length(); i < n; ++i) {
                    if (!this->AsUnion()->Get(i).Is(that))
                        return false;
                }
                return true;
            }

            // T <= (T1 \/ ... \/ Tn)  if  (T <= T1) \/ ... \/ (T <= Tn)
            if (that.IsUnion()) {
                for (int i = 0, n = that.AsUnion()->Length(); i < n; ++i) {
                    if (this->Is(that.AsUnion()->Get(i)))
                        return true;
                    if (i > 1 && this->IsRange())
                        return false; // Shortcut.
                }
                return false;
            }

            if (that.IsRange()) {
                return (this->IsRange() && Contains(that.AsRange(), this->AsRange()));
            }
            if (this->IsRange())
                return false;

            return this->SimplyEquals(that);
        }

        // Check if [this] and [that] overlap.
        bool Type::Maybe(Type that) const
        {
            DisallowHeapAllocation no_allocation;

            if (BitsetType::IsNone(this->BitsetLub() & that.BitsetLub()))
                return false;

            // (T1 \/ ... \/ Tn) overlaps T  if  (T1 overlaps T) \/ ... \/ (Tn overlaps T)
            if (this->IsUnion()) {
                for (int i = 0, n = this->AsUnion()->Length(); i < n; ++i) {
                    if (this->AsUnion()->Get(i).Maybe(that))
                        return true;
                }
                return false;
            }

            // T overlaps (T1 \/ ... \/ Tn)  if  (T overlaps T1) \/ ... \/ (T overlaps Tn)
            if (that.IsUnion()) {
                for (int i = 0, n = that.AsUnion()->Length(); i < n; ++i) {
                    if (this->Maybe(that.AsUnion()->Get(i)))
                        return true;
                }
                return false;
            }

            if (this->IsBitset() && that.IsBitset())
                return true;

            if (this->IsRange()) {
                if (that.IsRange()) {
                    return Overlap(this->AsRange(), that.AsRange());
                }
                if (that.IsBitset()) {
                    bitset number_bits = BitsetType::NumberBits(that.AsBitset());
                    if (number_bits == BitsetType::kNone) {
                        return false;
                    }
                    double min = std::max(BitsetType::Min(number_bits), this->Min());
                    double max = std::min(BitsetType::Max(number_bits), this->Max());
                    return min <= max;
                }
            }
            if (that.IsRange()) {
                return that.Maybe(*this); // This case is handled above.
            }

            if (this->IsBitset() || that.IsBitset())
                return true;

            return this->SimplyEquals(that);
        }

        // Return the range in [this], or [nullptr].
        Type Type::GetRange() const
        {
            DisallowHeapAllocation no_allocation;
            if (this->IsRange())
                return *this;
            if (this->IsUnion() && this->AsUnion()->Get(1).IsRange()) {
                return this->AsUnion()->Get(1);
            }
            return nullptr;
        }

        bool UnionType::Wellformed() const
        {
            DisallowHeapAllocation no_allocation;
            // This checks the invariants of the union representation:
            // 1. There are at least two elements.
            // 2. The first element is a bitset, no other element is a bitset.
            // 3. At most one element is a range, and it must be the second one.
            // 4. No element is itself a union.
            // 5. No element (except the bitset) is a subtype of any other.
            // 6. If there is a range, then the bitset type does not contain
            //    plain number bits.
            DCHECK_LE(2, this->Length()); // (1)
            DCHECK(this->Get(0).IsBitset()); // (2a)

            for (int i = 0; i < this->Length(); ++i) {
                if (i != 0)
                    DCHECK(!this->Get(i).IsBitset()); // (2b)
                if (i != 1)
                    DCHECK(!this->Get(i).IsRange()); // (3)
                DCHECK(!this->Get(i).IsUnion()); // (4)
                for (int j = 0; j < this->Length(); ++j) {
                    if (i != j && i != 0)
                        DCHECK(!this->Get(i).Is(this->Get(j))); // (5)
                }
            }
            DCHECK(!this->Get(1).IsRange() || (BitsetType::NumberBits(this->Get(0).AsBitset()) == BitsetType::kNone)); // (6)
            return true;
        }

        // -----------------------------------------------------------------------------
        // Union and intersection

        Type Type::Intersect(Type type1, Type type2, Zone* zone)
        {
            // Fast case: bit sets.
            if (type1.IsBitset() && type2.IsBitset()) {
                return NewBitset(type1.AsBitset() & type2.AsBitset());
            }

            // Fast case: top or bottom types.
            if (type1.IsNone() || type2.IsAny())
                return type1; // Shortcut.
            if (type2.IsNone() || type1.IsAny())
                return type2; // Shortcut.

            // Semi-fast case.
            if (type1.Is(type2))
                return type1;
            if (type2.Is(type1))
                return type2;

            // Slow case: create union.

            // Semantic subtyping check - this is needed for consistency with the
            // semi-fast case above.
            if (type1.Is(type2)) {
                type2 = Any();
            } else if (type2.Is(type1)) {
                type1 = Any();
            }

            bitset bits = type1.BitsetGlb() & type2.BitsetGlb();
            int size1 = type1.IsUnion() ? type1.AsUnion()->Length() : 1;
            int size2 = type2.IsUnion() ? type2.AsUnion()->Length() : 1;
            int size;
            if (base::bits::SignedAddOverflow32(size1, size2, &size))
                return Any();
            if (base::bits::SignedAddOverflow32(size, 2, &size))
                return Any();
            UnionType* result = UnionType::New(size, zone);
            size = 0;

            // Deal with bitsets.
            result->Set(size++, NewBitset(bits));

            RangeType::Limits lims = RangeType::Limits::Empty();
            size = IntersectAux(type1, type2, result, size, &lims, zone);

            // If the range is not empty, then insert it into the union and
            // remove the number bits from the bitset.
            if (!lims.IsEmpty()) {
                size = UpdateRange(Type::Range(lims, zone), result, size, zone);

                // Remove the number bits.
                bitset number_bits = BitsetType::NumberBits(bits);
                bits &= ~number_bits;
                result->Set(0, NewBitset(bits));
            }
            return NormalizeUnion(result, size, zone);
        }

        int Type::UpdateRange(Type range, UnionType* result, int size, Zone* zone)
        {
            if (size == 1) {
                result->Set(size++, range);
            } else {
                // Make space for the range.
                result->Set(size++, result->Get(1));
                result->Set(1, range);
            }

            // Remove any components that just got subsumed.
            for (int i = 2; i < size;) {
                if (result->Get(i).Is(range)) {
                    result->Set(i, result->Get(--size));
                } else {
                    ++i;
                }
            }
            return size;
        }

        RangeType::Limits Type::ToLimits(bitset bits, Zone* zone)
        {
            bitset number_bits = BitsetType::NumberBits(bits);

            if (number_bits == BitsetType::kNone) {
                return RangeType::Limits::Empty();
            }

            return RangeType::Limits(BitsetType::Min(number_bits),
                BitsetType::Max(number_bits));
        }

        RangeType::Limits Type::IntersectRangeAndBitset(Type range, Type bitset,
            Zone* zone)
        {
            RangeType::Limits range_lims(range.AsRange());
            RangeType::Limits bitset_lims = ToLimits(bitset.AsBitset(), zone);
            return RangeType::Limits::Intersect(range_lims, bitset_lims);
        }

        int Type::IntersectAux(Type lhs, Type rhs, UnionType* result, int size,
            RangeType::Limits* lims, Zone* zone)
        {
            if (lhs.IsUnion()) {
                for (int i = 0, n = lhs.AsUnion()->Length(); i < n; ++i) {
                    size = IntersectAux(lhs.AsUnion()->Get(i), rhs, result, size, lims, zone);
                }
                return size;
            }
            if (rhs.IsUnion()) {
                for (int i = 0, n = rhs.AsUnion()->Length(); i < n; ++i) {
                    size = IntersectAux(lhs, rhs.AsUnion()->Get(i), result, size, lims, zone);
                }
                return size;
            }

            if (BitsetType::IsNone(lhs.BitsetLub() & rhs.BitsetLub()))
                return size;

            if (lhs.IsRange()) {
                if (rhs.IsBitset()) {
                    RangeType::Limits lim = IntersectRangeAndBitset(lhs, rhs, zone);

                    if (!lim.IsEmpty()) {
                        *lims = RangeType::Limits::Union(lim, *lims);
                    }
                    return size;
                }
                if (rhs.IsRange()) {
                    RangeType::Limits lim = RangeType::Limits::Intersect(
                        RangeType::Limits(lhs.AsRange()), RangeType::Limits(rhs.AsRange()));
                    if (!lim.IsEmpty()) {
                        *lims = RangeType::Limits::Union(lim, *lims);
                    }
                }
                return size;
            }
            if (rhs.IsRange()) {
                // This case is handled symmetrically above.
                return IntersectAux(rhs, lhs, result, size, lims, zone);
            }
            if (lhs.IsBitset() || rhs.IsBitset()) {
                return AddToUnion(lhs.IsBitset() ? rhs : lhs, result, size, zone);
            }
            if (lhs.SimplyEquals(rhs)) {
                return AddToUnion(lhs, result, size, zone);
            }
            return size;
        }

        // Make sure that we produce a well-formed range and bitset:
        // If the range is non-empty, the number bits in the bitset should be
        // clear. Moreover, if we have a canonical range (such as Signed32),
        // we want to produce a bitset rather than a range.
        Type Type::NormalizeRangeAndBitset(Type range, bitset* bits, Zone* zone)
        {
            // Fast path: If the bitset does not mention numbers, we can just keep the
            // range.
            bitset number_bits = BitsetType::NumberBits(*bits);
            if (number_bits == 0) {
                return range;
            }

            // If the range is semantically contained within the bitset, return None and
            // leave the bitset untouched.
            bitset range_lub = range.BitsetLub();
            if (BitsetType::Is(range_lub, *bits)) {
                return None();
            }

            // Slow path: reconcile the bitset range and the range.
            double bitset_min = BitsetType::Min(number_bits);
            double bitset_max = BitsetType::Max(number_bits);

            double range_min = range.Min();
            double range_max = range.Max();

            // Remove the number bits from the bitset, they would just confuse us now.
            // NOTE: bits contains OtherNumber iff bits contains PlainNumber, in which
            // case we already returned after the subtype check above.
            *bits &= ~number_bits;

            if (range_min <= bitset_min && range_max >= bitset_max) {
                // Bitset is contained within the range, just return the range.
                return range;
            }

            if (bitset_min < range_min) {
                range_min = bitset_min;
            }
            if (bitset_max > range_max) {
                range_max = bitset_max;
            }
            return Type::Range(range_min, range_max, zone);
        }

        Type Type::NewConstant(double value, Zone* zone)
        {
            if (RangeType::IsInteger(value)) {
                return Range(value, value, zone);
            } else if (IsMinusZero(value)) {
                return Type::MinusZero();
            } else if (/*std::*/isnan(value)) {
                return Type::NaN();
            }

            DCHECK(OtherNumberConstantType::IsOtherNumberConstant(value));
            return OtherNumberConstant(value, zone);
        }

        Type Type::NewConstant(JSHeapBroker* broker, Handle<i::Object> value,
            Zone* zone)
        {
            ObjectRef ref(broker, value);
            if (ref.IsSmi()) {
                return NewConstant(static_cast<double>(ref.AsSmi()), zone);
            }
            if (ref.IsHeapNumber()) {
                return NewConstant(ref.AsHeapNumber().value(), zone);
            }
            if (ref.IsString() && !ref.IsInternalizedString()) {
                return Type::String();
            }
            return HeapConstant(ref.AsHeapObject(), zone);
        }

        Type Type::Union(Type type1, Type type2, Zone* zone)
        {
            // Fast case: bit sets.
            if (type1.IsBitset() && type2.IsBitset()) {
                return NewBitset(type1.AsBitset() | type2.AsBitset());
            }

            // Fast case: top or bottom types.
            if (type1.IsAny() || type2.IsNone())
                return type1;
            if (type2.IsAny() || type1.IsNone())
                return type2;

            // Semi-fast case.
            if (type1.Is(type2))
                return type2;
            if (type2.Is(type1))
                return type1;

            // Slow case: create union.
            int size1 = type1.IsUnion() ? type1.AsUnion()->Length() : 1;
            int size2 = type2.IsUnion() ? type2.AsUnion()->Length() : 1;
            int size;
            if (base::bits::SignedAddOverflow32(size1, size2, &size))
                return Any();
            if (base::bits::SignedAddOverflow32(size, 2, &size))
                return Any();
            UnionType* result = UnionType::New(size, zone);
            size = 0;

            // Compute the new bitset.
            bitset new_bitset = type1.BitsetGlb() | type2.BitsetGlb();

            // Deal with ranges.
            Type range = None();
            Type range1 = type1.GetRange();
            Type range2 = type2.GetRange();
            if (range1 != nullptr && range2 != nullptr) {
                RangeType::Limits lims = RangeType::Limits::Union(RangeType::Limits(range1.AsRange()),
                    RangeType::Limits(range2.AsRange()));
                Type union_range = Type::Range(lims, zone);
                range = NormalizeRangeAndBitset(union_range, &new_bitset, zone);
            } else if (range1 != nullptr) {
                range = NormalizeRangeAndBitset(range1, &new_bitset, zone);
            } else if (range2 != nullptr) {
                range = NormalizeRangeAndBitset(range2, &new_bitset, zone);
            }
            Type bits = NewBitset(new_bitset);
            result->Set(size++, bits);
            if (!range.IsNone())
                result->Set(size++, range);

            size = AddToUnion(type1, result, size, zone);
            size = AddToUnion(type2, result, size, zone);
            return NormalizeUnion(result, size, zone);
        }

        // Add [type] to [result] unless [type] is bitset, range, or already subsumed.
        // Return new size of [result].
        int Type::AddToUnion(Type type, UnionType* result, int size, Zone* zone)
        {
            if (type.IsBitset() || type.IsRange())
                return size;
            if (type.IsUnion()) {
                for (int i = 0, n = type.AsUnion()->Length(); i < n; ++i) {
                    size = AddToUnion(type.AsUnion()->Get(i), result, size, zone);
                }
                return size;
            }
            for (int i = 0; i < size; ++i) {
                if (type.Is(result->Get(i)))
                    return size;
            }
            result->Set(size++, type);
            return size;
        }

        Type Type::NormalizeUnion(UnionType* unioned, int size, Zone* zone)
        {
            DCHECK_LE(1, size);
            DCHECK(unioned->Get(0).IsBitset());
            // If the union has just one element, return it.
            if (size == 1) {
                return unioned->Get(0);
            }
            bitset bits = unioned->Get(0).AsBitset();
            // If the union only consists of a range, we can get rid of the union.
            if (size == 2 && bits == BitsetType::kNone) {
                if (unioned->Get(1).IsRange()) {
                    return Type::Range(unioned->Get(1).AsRange()->Min(),
                        unioned->Get(1).AsRange()->Max(), zone);
                }
            }
            unioned->Shrink(size);
            SLOW_DCHECK(unioned->Wellformed());
            return Type(unioned);
        }

        int Type::NumConstants() const
        {
            DisallowHeapAllocation no_allocation;
            if (this->IsHeapConstant() || this->IsOtherNumberConstant()) {
                return 1;
            } else if (this->IsUnion()) {
                int result = 0;
                for (int i = 0, n = this->AsUnion()->Length(); i < n; ++i) {
                    if (this->AsUnion()->Get(i).IsHeapConstant())
                        ++result;
                }
                return result;
            } else {
                return 0;
            }
        }

        // -----------------------------------------------------------------------------
        // Printing.

        const char* BitsetType::Name(bitset bits)
        {
            switch (bits) {
#define RETURN_NAMED_TYPE(type, value) \
    case k##type:                      \
        return #type;
                PROPER_BITSET_TYPE_LIST(RETURN_NAMED_TYPE)
                INTERNAL_BITSET_TYPE_LIST(RETURN_NAMED_TYPE)
#undef RETURN_NAMED_TYPE

            default:
                return nullptr;
            }
        }

        void BitsetType::Print(std::ostream& os, // NOLINT
            bitset bits)
        {
            DisallowHeapAllocation no_allocation;
            const char* name = Name(bits);
            if (name != nullptr) {
                os << name;
                return;
            }

            // clang-format on
            static const bitset named_bitsets[] = {
#define BITSET_CONSTANT(type, value) k##type,
                INTERNAL_BITSET_TYPE_LIST(BITSET_CONSTANT)
                    PROPER_BITSET_TYPE_LIST(BITSET_CONSTANT)
#undef BITSET_CONSTANT
            };
            // clang-format on

            bool is_first = true;
            os << "(";
            for (int i(arraysize(named_bitsets) - 1); bits != 0 && i >= 0; --i) {
                bitset subset = named_bitsets[i];
                if ((bits & subset) == subset) {
                    if (!is_first)
                        os << " | ";
                    is_first = false;
                    os << Name(subset);
                    bits -= subset;
                }
            }
            DCHECK_EQ(0, bits);
            os << ")";
        }

        void Type::PrintTo(std::ostream& os) const
        {
            DisallowHeapAllocation no_allocation;
            if (this->IsBitset()) {
                BitsetType::Print(os, this->AsBitset());
            } else if (this->IsHeapConstant()) {
                os << "HeapConstant(" << Brief(*this->AsHeapConstant()->Value()) << ")";
            } else if (this->IsOtherNumberConstant()) {
                os << "OtherNumberConstant(" << this->AsOtherNumberConstant()->Value()
                   << ")";
            } else if (this->IsRange()) {
                std::ostream::fmtflags saved_flags = os.setf(std::ios::fixed);
                std::streamsize saved_precision = os.precision(0);
                os << "Range(" << this->AsRange()->Min() << ", " << this->AsRange()->Max()
                   << ")";
                os.flags(saved_flags);
                os.precision(saved_precision);
            } else if (this->IsUnion()) {
                os << "(";
                for (int i = 0, n = this->AsUnion()->Length(); i < n; ++i) {
                    Type type_i = this->AsUnion()->Get(i);
                    if (i > 0)
                        os << " | ";
                    os << type_i;
                }
                os << ")";
            } else if (this->IsTuple()) {
                os << "<";
                for (int i = 0, n = this->AsTuple()->Arity(); i < n; ++i) {
                    Type type_i = this->AsTuple()->Element(i);
                    if (i > 0)
                        os << ", ";
                    os << type_i;
                }
                os << ">";
            } else {
                UNREACHABLE();
            }
        }

#ifdef DEBUG
        void Type::Print() const
        {
            StdoutStream os;
            PrintTo(os);
            os << std::endl;
        }
        void BitsetType::Print(bitset bits)
        {
            StdoutStream os;
            Print(os, bits);
            os << std::endl;
        }
#endif

        BitsetType::bitset BitsetType::SignedSmall()
        {
            return SmiValuesAre31Bits() ? kSigned31 : kSigned32;
        }

        BitsetType::bitset BitsetType::UnsignedSmall()
        {
            return SmiValuesAre31Bits() ? kUnsigned30 : kUnsigned31;
        }

        // static
        Type Type::Tuple(Type first, Type second, Type third, Zone* zone)
        {
            TupleType* tuple = TupleType::New(3, zone);
            tuple->InitElement(0, first);
            tuple->InitElement(1, second);
            tuple->InitElement(2, third);
            return FromTypeBase(tuple);
        }

        // static
        Type Type::OtherNumberConstant(double value, Zone* zone)
        {
            return FromTypeBase(OtherNumberConstantType::New(value, zone));
        }

        // static
        Type Type::HeapConstant(JSHeapBroker* broker, Handle<i::Object> value,
            Zone* zone)
        {
            return FromTypeBase(
                HeapConstantType::New(HeapObjectRef(broker, value), zone));
        }

        // static
        Type Type::HeapConstant(const HeapObjectRef& value, Zone* zone)
        {
            return HeapConstantType::New(value, zone);
        }

        // static
        Type Type::Range(double min, double max, Zone* zone)
        {
            return FromTypeBase(RangeType::New(min, max, zone));
        }

        // static
        Type Type::Range(RangeType::Limits lims, Zone* zone)
        {
            return FromTypeBase(RangeType::New(lims, zone));
        }

        // static
        Type Type::Union(int length, Zone* zone)
        {
            return FromTypeBase(UnionType::New(length, zone));
        }

        const HeapConstantType* Type::AsHeapConstant() const
        {
            DCHECK(IsKind(TypeBase::kHeapConstant));
            return static_cast<const HeapConstantType*>(ToTypeBase());
        }

        const OtherNumberConstantType* Type::AsOtherNumberConstant() const
        {
            DCHECK(IsKind(TypeBase::kOtherNumberConstant));
            return static_cast<const OtherNumberConstantType*>(ToTypeBase());
        }

        const RangeType* Type::AsRange() const
        {
            DCHECK(IsKind(TypeBase::kRange));
            return static_cast<const RangeType*>(ToTypeBase());
        }

        const TupleType* Type::AsTuple() const
        {
            DCHECK(IsKind(TypeBase::kTuple));
            return static_cast<const TupleType*>(ToTypeBase());
        }

        const UnionType* Type::AsUnion() const
        {
            DCHECK(IsKind(TypeBase::kUnion));
            return static_cast<const UnionType*>(ToTypeBase());
        }

        std::ostream& operator<<(std::ostream& os, Type type)
        {
            type.PrintTo(os);
            return os;
        }

    } // namespace compiler
} // namespace internal
} // namespace v8
